I think San Francisco is a great walking city, so many of my suggestions revolve around seeing the city on foot. I'd recommend walking across the Gold Gate Bridge, walking through the Presidio and along the Embarcadero, walking up the stairways of Russian Hill or Corona Heights, along Valencia Street (if you like boutique-type shops and to get an affordable lunch) and to Dolores Park.

Other suggestions are to take a quick boat ride under the Golden Gate and around Alcatraz from one of the boats docked at Fisherman's Wharf. The Marin Headlands and Muir Woods are gorgeous and close by, but taking a car or tour is generally the easiest way to get there.

Thank you very much for suggestions.

I'd also add some less well-known things like hiking in the Marin Headlands, the Ferry Building Farmer's Market, seeing a concert at the Fillmore, taking in the view from atop Twin Peaks and Coit Tower, having a burrito in the Mission, and watching the surf at Ocean Beach.